Iraqis have voted in the country's first elections since the 2011 U.S. military withdrawal, under tight security aimed at curbing violence from a revived al-Qaida insurgency.

There were no reports of major violence Saturday, prompting a U.S. embassy statement congratulating the Iraqi people "for reaffirming their commitment to democracy and a future free of fear and intimidation."

The statement also called Saturday's contests for local councils "a clear step forward...and a strong rejection of the violent extremists" behind a spate of pre-election bombings that killed more than 50 people and wounded about 200 others in the past week.

Voting was limited to 12 of Iraq's 18 provinces, following political disagreements in four provinces, and after authorities last month delayed voting in the largely Sunni Anbar and Ninewa provinces.

The delays in Anbar and Ninewa -- sites of recent anti-government protests -- have raised questions about the motives of Shi'ite Prime Minister Nouri al-Maliki's government for the postponements.

The U.S. embassy urged the government in Baghdad to reschedule those polls as soon as possible.

Saturday's elections are widely viewed as a measure of the strength of political parties ahead of parliamentary elections in 2014.

Around 8,000 local candidates are running for 378 positions in provincial councils. Vote counting is expected to begin Sunday.